Ever since it burst upon the world six years back,
Arcade Fire hasn't been a band whose place in music you could track on a standard cultural GPS.

Instead, you'd need multiple maps, a kind of anthropological atlas. Its geographic scope would range from artsy Montreal epicentre Mile End to the outskirts of Houston to the shantytowns of Port au Prince. It would include headings such as Family Ties, Social Circles and Generational Divides; Venn diagrams of genre overlap; trajectories of spiritual inquiry; and flows of income redistribution.

Also handy, given the group's preoccupation with personal and civilizational mortality, might be blueprints of the Underworld. What's more, on each map you'd have to triangulate seemingly mutually exclusive co-ordinates.

Before making this record, I felt the least connected I ever had to where I grew up and where I lived the longest.
Win Butler

This is a seven-strong Canadian collective led by an American, 30-year-old Win Butler. He founded it with his wife, Régine Chassagne, the Quebec-born daughter of Haitian refugees. Their best songs locate places (peaks in the clouds, or maybe caverns in the earth) where elation and fear, estrangement and communalism, grandeur and the homespun somehow become one.

And while methodically rejecting commercialism and sticking with an indie label (the small but illustrious Merge Records, of North Carolina), Arcade Fire has been paradoxically successful - not on the mainstream-radio level of, say, Nickelback, but leagues beyond other baggy northern collectives such as the New Pornographers or Broken Social Scene.

Arcade Fire's first album, 2004's
Funeral, was named the best of the decade by Rolling Stone, and second only to Radiohead's
Kid A by Pitchfork. Its second,
Neon Bible, in 2007, entered the Billboard charts at No. 2. As veteran Canadian music writer Larry LeBlanc puts it, "They shook up the industry worldwide. They unrolled the cusp of this non-traditional-exposure route."

Yet with their third album,
The Suburbs, due out Tuesday, Arcade Fire seems, on some levels, to be decamping even from its place as the very model of the 2000-something indie band.

In the early days, the group seemed to have sprung direct from the skull of post-2001 youth culture when it was recuperating from multiple, disillusioning blows. As if to emphasize the point, the players often wore motorcycle helmets onstage so they could beat each other with drumsticks as a perversely jubilant form of percussion.

It had its throng of members (the core seven easily expand to 10 or 12 on tour), its multi-instrumental bombast (accordions, violins, parade drums, glockenspiels, myriad guitars, yelping vocal leads and children's-chorus harmonies), its social and poetic high-mindedness, and a guerrilla-theatre spirit that made shows a mix of schoolyard romp and pagan purification rite.

Toronto's Owen Pallett, whose link as string arranger and guest violinist with Arcade Fire gave a jet boost to his own solo career, recalls, "Sometimes you just know, 'Oh my God, this is going to be really, really popular.' "

The embrace of
Funeral took the band around the globe and left its members comfortably well-off - this year they've pledged, for instance, to match fan donations of up to $1-million for Haitian aid. They are also, less comfortably, well-known: To hear Butler talk of the Internet is to hear a battered-down man, likely due to some of the fan backlash against the relatively dense dourness of the God-and-Bush-bothered
Neon Bible.

And unnervingly well-connected: Arcade Fire has shared stages with David Bowie, David Byrne, U2 and Bruce Springsteen, who, like Peter Gabriel, has covered one of its songs.

This month, when the band was invited by YouTube to inaugurate a new streaming-concert series with the second of its two shows next week at New York's Madison Square Garden (Madison Square Garden!), Butler was able to get a "major, life-long inspiration" - Terry Gilliam, former Monty Python animator and maker of
Brazil - to direct it. Just by asking.

Little wonder Butler sings, on the new record, "Now our lives are changing fast/ Hope that something pure can last."

Drafted during a year-long break and recorded over the course of another year, the new album is the work of an ensemble that's been through transformations and needed to stand back and process. Needed, in other words, to redraw its own map.

"I very much see it as trying to connect where you're from and where you are, to have that kind of make sense," says Butler. "Before making this record, I felt the least connected I ever had to where I grew up and where I lived the longest."